Hyperbolic normal stochastic volatility model

For option pricing models and heavy-tailed distributions, this study proposes a continuous-time stochastic volatility model based on an arithmetic Brownian motion: a one-parameter extension of the normal stochastic alpha-beta-rho (SABR) model. Using two generalized Bougerol's identities in the...

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Bibliographic Details
Published in:arXiv.org 2018-09
Main Authors: Choi, Jaehyuk, Liu, Chenru, Seo, Byoung Ki
Format: Article
Language:English
Subjects:
Brownian motion
Computer simulation
Monte Carlo simulation
Stochastic models
Stochastic processes
Volatility
Online Access:Get full text
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Summary:For option pricing models and heavy-tailed distributions, this study proposes a continuous-time stochastic volatility model based on an arithmetic Brownian motion: a one-parameter extension of the normal stochastic alpha-beta-rho (SABR) model. Using two generalized Bougerol's identities in the literature, the study shows that our model has a closed-form Monte-Carlo simulation scheme and that the transition probability for one special case follows Johnson's \(S_U\) distribution---a popular heavy-tailed distribution originally proposed without stochastic process. It is argued that the \(S_U\) distribution serves as an analytically superior alternative to the normal SABR model because the two distributions are empirically similar.
ISSN:2331-8422
DOI:10.48550/arxiv.1809.04035